@inproceedings{0da2fadcb5f542b2b2e6e2d52e6cfb8f,

title = "Relative polynomial closure and monadically Krull monoids of integer-valued polynomials",

abstract = "Let D be a Krull domain and Int(D) the ring of integer-valued polynomials on D. For any f∈Int(D), we explicitly construct a divisor homomorphism from [[f]], the divisor-closed submonoid of Int(D) generated by f, to a finite sum of copies of (N0,+). This implies that [[f]] is a Krull monoid. For V a discrete valuation domain, we give explicit divisor theories of various submonoids of Int(V). In the process, we modify the concept of polynomial closure in such a way that every subset of D has a finite polynomially dense subset . The results generalize to Int(S,V), the ring of integer-valued polynomials on a subset, provided S does not have isolated points in v-adic topology ",

keywords = "commutative rings, factorization, monoids, divisor theory, arithmetic",

author = "Sophie Frisch",

year = "2016",

doi = "10.1007/978-3-319-38855-7_6",

language = "English",

isbn = "978-3-319-38853-3",

series = " Springer Proceedings in Mathematics & Statistics",

publisher = "Springer International Publishing AG ",

pages = "145--157",

editor = "Scott Chapman and Marco Fontana and Alfred Geroldinger and Bruce Olberding",

booktitle = "Multiplicative Ideal Theory and Factorization Theory",

address = "Switzerland",

}